Election 2020 updates: Biden warns of 'dark winter,' pushes masks in pandemic plan

Trump’s lawyer, Rudy Giuliani, on Saturday vowed to file a lawsuit Monday to challenge the conduct of elections officials in Pennsylvania.

In comments laced with vague and unfounded allegations of voter fraud in Pennsylvania, Giuliani alleged that the Trump campaign was deprived of the ability to watch the ballots being processed. And he said the campaign would make similar allegations in other states that could lead the campaign to make the case a “massive nation-wide lawsuit.”

“We were deprived of the right to inspect if a single one of those ballots is legitimate,” Giuliani said. “That is unheard of, it’s illegal, it’s unconstitutional, and we will be bringing an action challenging that.”

The Trump campaign has now brought multiple similar charges into court since Election Day and all but one of the cases has been rejected – in Michigan and Nevada. In Pennsylvania, a state judge ordered election officials to allow observers to move closer to poll workers, but a federal judge refused to halt the count based on the claims.

In several of the cases, judges have used strikingly similar language to criticize Trump campaign attorneys for bringing the cases without sufficient evidence. Biden attorney Bob Bauer on Thursday called the lawsuits "meritless."

Observers are permitted to watch the processing of ballots in most states, including Pennsylvania, but not allowed to intervene as the ballots are processed. They can note any irregularities and report them back to their campaign’s legal team.

Giuliani alleged that Trump campaign representatives were not close enough to see if ballots had errors or irregularities. But for days, Trump campaign officials have not been able to explain what remedy they could expect should a court agree that they were not given sufficient access to watch the poll workers open envelopes of mail-in ballots and inspect them to make sure signatures match, dates are accurate, and the secrecy envelope is used properly.

-ABC News' Matt Mosk and Alex Hosenball

Trump, who is golfing on Saturday, released a defiant statement through his campaign, claiming, "this election is far from over."

Trump blasted Biden for "rushing to falsely pose as the winner."

Following media projections, Biden changed his Twitter bio to "President-elect." Biden said in a statement Saturday, "I am honored and humbled by the trust the American people have placed in me."

Trump also touted the coming legal fight.

"Beginning Monday, our campaign will start prosecuting our case in court to ensure election laws are fully upheld and the rightful winner is seated," he said. "The American People are entitled to an honest election: that means counting all legal ballots, and not counting any illegal ballots."

The president again pushed unfounded claims that "Only a party engaged in wrongdoing would unlawfully keep observers out of the count room – and then fight in court to block their access."

Asked if Trump would call Biden to concede, White House deputy press secretary Judd Deere said: “No scheduling updates. The campaign has released a statement from the president.”

ABC News can characterize Joe Biden as the apparent winner in Pennsylvania -- a win that makes him president-elect. Based on these numbers and those in other states, Joe Biden will be the next President of the United States.

ABC News was able to characterize Biden as the apparent winner of Pennsylvania after the state, as of 11:35 a.m., put Biden ahead with 49.6% (3,345,724 votes) over Trump's 49.1% (3,311,310 votes).

Biden was at home with his family when he learned of the news, a Biden aide told ABC News. Biden is expected to address the nation Saturday night.

Biden said in a statement Saturday, "I am honored and humbled by the trust the American people have placed in me and in Vice President-elect Harris. In the face of unprecedented obstacles, a record number of Americans voted. Proving once again, that democracy beats deep in the heart of America. With the campaign over, it’s time to put the anger and the harsh rhetoric behind us and come together as a nation. It’s time for America to unite. And to heal. We are the United States of America. And there’s nothing we can’t do, if we do it together."

Saturday marks 48 years to the day that Biden was elected in his first Senate race. Biden, then 29 years old, won his first Senate election on Nov. 7, 1972.

For first time in history, the first and second in line to the presidency will be women: Sen. Kamala Harris as vice president followed by House Speaker Nancy Pelosi.

Harris tweeted a video showing her on the phone with Biden. "We did it, Joe," she said. "You're going to be the next president of the United States."

Harris' husband, Doug Emhoff, tweeted, "So proud of you."

Harris spoke on the phone Saturday with former President Barack Obama, former Secretary of State Hillary Clinton and House Speaker Nancy Pelosi.

The White House declined to comment on several news organizations projecting Biden as the apparent winner.

Biden is leading Arizona by 20,573 votes after Maricopa County, home to Phoenix, dropped 48,517 more ballots Saturday morning.

Biden is at 49.5% compared to Trump's 48.9%.

About 43,000 ballots are still outstanding in Maricopa County.

Arizona has 11 Electoral College votes.

In a tweet Saturday morning, Arizona Secretary of State Katie Hobbs defended the flow of information coming from her office throughout the election.

-ABC News' Meg Cunningham